Smooth empirical Bayes estimation for continuous distributions

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Abstract
Although the conditions for application of the technique of empirical Bayes estimation of the parameter of a distribution may exist, the form of the prior distribution is generally unknown. This often creates major difficultics in the determination of empirical Bayes estimators. The simple device of approximating the prior distribution by a stop function is used to overcome this problem and to obtain smooth empirical Bayes estimators. This paper supplements earlier work by considering continuous distributions and multiple past and current observations. The effectiveness of the proposed smooth empirical Bayes estimators is examined, and the results indicate that they can be substantially better than optimum non-Bayes estimators, even when the amount of past data is small.

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